In general Pre-emergence application of Atrazine (Atratraf 50 wp, Gesaprim 500 fw) @ of 1.0-1.5 kg a.i ha-1 in 600 litre water, Alachlor (Lasso) @ 2-2.5 kg a.i ha-1, Metolachlor (Dual) @ 1.5-2.0 kg a.i ha-1 , Pendamethalin (Stomp) @ 1-1.5 kg a.i. ha-1 are effective way for control of many annual and broad leaved weeds in maize crop.
However, One to two hoeing are recommended for aeration and uprooting of the remaining weeds, if any.
For zero tillage maize production it is practiced that pre-plant application (10-15 days prior to seeding) of non-selective herbicides viz., Glyphosate @ 1.0 kg a.i. ha-1 in 400-600 litre water or Paraquat @ 0.5 kg a.i. ha-1 in 600 litre water can do the wonder.
However, combination of both practice ( i.e. chemical + mechanical) certainly pave the way for efficient weed management.
Being C4 crop its growth and development is faster tan the weeds in the most of cases, during its life cycle, except during initial phases. Once maize comes at knee height weed management has no meaning except aesthetic value, until unless some bio-agent is not harboring on weeds.
As far as I understood, you asked for post-em products. Of course, to give you a proper answer, it would be necessary to know the weed spectrum, you want to control. But in general, a group of actives with a broad spectrum of mainly annual broadleaf weeds and some annual grassweeds (Panicum species, also some efficacy sometmes on Poa) is the group of triketons (mesotrione, tembotrione, sulcotrione, topramezone). Bromoxynil would help on some species like persicaria ssp.. For some perennial broadleaf weeds like convolvolus-species or calystegia dicamba can help. The adding of some atrauine/terbuthylazin or metolachlor can increase the efficacy also on post-em use due to some synergistic effects.
I think this recommendation of herbicides for weed control in maize is depending on weed flora and soil properties. Anyway post-emergence herbicides including nicosulfuron 40 g L−1 suspension concentrate (SC), topramezone 336 g L−1 SC, and the combination of mesotrione/nicosulfuron 105 g L−1 oil dispersion can effectively control broadleaved and grass weeds in maize at the 2- to 3-leaf and 4- to 5-leaf stages of weeds.
To control sedges, grasses and trianthema portulacastrum effectively you can use 55% Mesotrione+atrazine and to control only sedges you can use halosulfuran as post-emergence herbicides.
Tembotrione 120 g/ha is also an effective post-emergence herbicide in maize. I found it quite effective even upto 50DAS maize. One may see my publications on weed control in maize for further quarry.
For Kharif maize, pre-emergence application of atrazine (750/1000 g/ha) or alachlor (2000) g/ha followed by tembotrione + Surfactant (120 g/ha) at 30-35 DAS (days after sowing) gave effective control of complex weed flora.
Tembotrione + surfactant is very effective if applied at 15-20 DAS of the maize crop. There is regeneration of Cyprus species. If Cyperus species is problem apply halosulfuron methy @67.5g/ha (sempra 90 g/ha product dose) at 20-30 DAP or at 3-5 leaf stage of Cyperus. Do not apply this herbicide if maize is intercropped with any other crop
Tembotrione and Topramizon are very effective in maize. But I did not used these herbicides in pearl millet. Dr RS Bana is right person to comment on this as he is renowned pearl millet agronomist.
Tembotrione is widely used post emergence herbicide in maize and sugarcane. Another herbicide Topramezone is also widely used as post emergence herbicide in maize and sugarcane. Topramezone can also be applied at 3-5 leaf stage of weed.
Atrazine 50 WP @ 0.5- 0.75kg a.i./ha as PE followed by Tembotrione 42 SC@ 120 g a.i./ha as PoE at 25 DAS for rainy season maize and 35 DAS for winter season maize.