The whitefly (Bemisia tabaci) is not preying host for predatory mite (Phytoseiulus persimilis) but looking to its cannabilistic nature, when spider mite prey is unavailable,  it may attack over whitefly. Therefore you are requested to verify then proceed for large scale release of this predatory mite. I noticed that It feeds on thrips otherwise it is specialized predator of tetranichids. 

Phytoseiulus persimilis is a predator of TSSM two spotted spider mite

But not White fly.

No, Phytoseiulus  persimilis do not prey on Bemisia tabaci eggs. You should try Chrysoperla carnea (Neuroptera; Chrysopidae), Delphastus pusillus , Harmonia axyridis and Azya orbigera (Coleoptera: Coccinelidae). They will feed  on whitefly eggs, nymphs, and adults of Bemisia tabaci. Also the bug Macrolophus caliginosus (Hemiptera: Miridae) is polyphagous and feeds on eggs, pupae and adults of B. tabaci.

P. persimilis is a highly specific predator to mites of genus Tetranychus and will probably never feed B. tabaci eggs.

Hi Pijush

Some references 1

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFgg9MAY&url=http%3A%2F%2Fjournals.plos.org%2Fplosone%2Farticle%3Fid%3D10.1371%2Fjournal.pone.0138820&usg=AOvVaw1VWXbHNLOBjNnIV97WPZzX

2

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghHMAc&url=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4593607%2F&usg=AOvVaw07bjR-huTmgYgTtE1IoDGy

3

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghNMAg&url=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3016914%2F&usg=AOvVaw0DzbFnq7xKSnYMpXoChemn

4

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghWMAk&url=https%3A%2F%2Fwww.nature.com%2Farticles%2Fsrep22992&usg=AOvVaw2xz-_CkU65MJTp8YbUqr73

5

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=11&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghhMAo&url=https%3A%2F%2Fpdfs.semanticscholar.org%2F675c%2F1ddb9be78f1fc4c95985a4eb5d606788352c.pdf&usg=AOvVaw30VKa6Nn-sNbk2apqxIE73

6

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=12&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghqMAs&url=https%3A%2F%2Fag.umass.edu%2Fgreenhouse-floriculture%2Ffact-sheets%2Fbiological-control-greenhouse-pests-their-natural-enemies&usg=AOvVaw1P3efTggdKKK8UqTmYJCka

7

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=13&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghwMAw&url=http%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Ffull%2F10.1080%2F01647954.2017.1349177%3Fsrc%3Drecsys&usg=AOvVaw3hhjHB5ZMj4COvKgVRuJzO

8

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=14&cad=rja&uact=8&ved=0ahUKEwj1nu2dqaXYAhVIo6QKHRZ4BO4QFghyMA0&url=https%3A%2F%2Flink.springer.com%2Fcontent%2Fpdf%2F10.1007%2F978-94-017-0611-7_31.pdf&usg=AOvVaw3lLsOnT8mNTmwgx2K0UTKv

9

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=11&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCCYwAA&url=http%3A%2F%2Fwww.bioone.org%2Fdoi%2Fpdf%2F10.11158%2Fsaa.21.3.3&usg=AOvVaw0Qbboicil1MZySb-SbsCoL

10

https://books.google.iq/books?id=0sLTMbNswecC&pg=PA377&lpg=PA377&dq=Phytoseiulus+persimilis+prey+Bemisia+tabaci+egg&source=bl&ots=7Ts7RYk8v5&sig=ZX7s7kwh5V9GBesrrR2AHxIk5Jk&hl=en&sa=X&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChDoAQgvMAE

11

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=13&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCDQwAg&url=https%3A%2F%2Fbiocontrol.entomology.cornell.edu%2Fpredators%2FPhytoseiulus.php&usg=AOvVaw0uHoc4ADDlaUZMBecoN55a

12

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=14&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCDowAw&url=http%3A%2F%2Fwww.scialert.net%2Ffulltext%2F%3Fdoi%3Dje.2011.52.62%26org%3D10&usg=AOvVaw1TrGPmb-Y_Lt7rjR8h9M2T

13

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=15&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCEAwBA&url=http%3A%2F%2Fwww.alamy.com%2Fstock-photo%2Fpredatory-mite.html&usg=AOvVaw1UjgRvPQNsB5IjIvlVfTVU

14

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=16&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCEUwBQ&url=http%3A%2F%2Fwww.iobc-wprs.org%2Fpub%2Fbulletins%2Fbulletin_2014_102_table_of_contents_abstracts.pdf&usg=AOvVaw0sy7T9CLuXPsK6GRkcWuG8

15

https://books.google.iq/books?id=AnPvCAAAQBAJ&pg=PA415&lpg=PA415&dq=Phytoseiulus+persimilis+prey+Bemisia+tabaci+egg&source=bl&ots=bUBUbxA0RU&sig=vJLIj4sPanRlNGVu2iUyfCBFddY&hl=en&sa=X&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChDoAQhMMAY

16

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=19&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCFMwCA&url=http%3A%2F%2Faprs.iobc.info%2F20160515-19_IOBC-APRS_WG_predatory_mites_1st_workshop_abstact_book.pdf&usg=AOvVaw36SBsiqhG2GwqGXFvpXJA_

17

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=20&cad=rja&uact=8&ved=0ahUKEwjnwa_BqqXYAhWJ46QKHYC1ADY4ChAWCFowCQ&url=https%3A%2F%2Fwww.appliedbio-nomics.com%2Fwp-content%2Fuploads%2F200-persimilis05.pdf&usg=AOvVaw0ImNAk_LfvgTw0gYYrxx1d

18

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=21&cad=rja&uact=8&ved=0ahUKEwjJ2qjdq6XYAhVSpKQKHXGFAEI4FBAWCCYwAA&url=http%3A%2F%2Faprs.iobc.info%2F20160515-19_IOBC-APRS_WG_predatory_mites_1st_workshop_abstact_book.pdf&usg=AOvVaw36SBsiqhG2GwqGXFvpXJA_

19

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=22&cad=rja&uact=8&ved=0ahUKEwjJ2qjdq6XYAhVSpKQKHXGFAEI4FBAWCC0wAQ&url=https%3A%2F%2Fwww.appliedbio-nomics.com%2Fwp-content%2Fuploads%2F200-persimilis05.pdf&usg=AOvVaw0ImNAk_LfvgTw0gYYrxx1d

20

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=24&cad=rja&uact=8&ved=0ahUKEwjJ2qjdq6XYAhVSpKQKHXGFAEI4FBAWCDgwAw&url=http%3A%2F%2Fwww.abim.ch%2Ffileadmin%2Fabim%2Fdocuments%2Fpresentations2006%2Fsession3%2F3_Bolckmans_ABIM-Lucerne_2006.pdf&usg=AOvVaw2gUmcIwaa3WGoj8h_vPcOl

I think the predatory mites Phytoseiulus attack tetranychus spiders

for Bemicia it can be displaced by bassiana