There's a few things that can cause phase inversion with phenol/chloroform extraction. What kind of samples did you extract from and is it possible that something heavy and water-soluble is in there? (Eg: sugar, salt, PEG, glycerol, etc). What was the ratio of trizol to sample? Was your centrifuge cooled to 4C before you did the cold spin?
This previous Researchgate discussion of the phase inversion problem may help. Temperature or salts may be the problem. Solutions are suggested. https://www.researchgate.net/post/How-to-fix-phase-inversion-when-doing-Trizol-extractions-RNA-DNA-proteins
A colleague of mine had the same problem when she didn't vortex properly after adding the chloroform to the trizol (the sample must no longer be clear after mixing) before the centrifugation. I think this wasn't suggested in the link above. Good luck!
Laura Leighton I used HEK293, and there is nothing heavy in the culture. I used 0.4 ml of Trizol for a 35mm plate with a 95% of confluency. And the centrifuge was previously cold to 4ºC.