Does proliferate affect poison counters on players as well as counters on permanents?

Proliferate explicitly covers both players and permanents. Under CR 701.27b, when you proliferate you choose any number of players and/or permanents that already have at least one counter on them, then give each one additional counter of each kind that player or permanent already has.

Poison counters sit on players, not on permanents, so they are handled by the 'players' half of the proliferate instruction. If a player already has one or more poison counters, you may choose that player when you proliferate and they will receive one additional poison counter (CR 701.27b, 122.1).

The same single proliferate event can simultaneously add poison counters to a player AND loyalty counters to a planeswalker AND +1/+1 counters to a creature — each chosen object gets one more of every counter type it already has.

Concrete example: Your opponent has 3 poison counters and controls a Crystalline Crawler with 2 +1/+1 counters. You cast Thrummingbird and deal combat damage, triggering proliferate. You choose both your opponent and the Crawler. Your opponent goes to 4 poison counters; the Crawler goes to 3 +1/+1 counters.

Note the key restriction: the player or permanent must already have at least one counter of the type before you can add another. Proliferate cannot place a brand-new counter type that wasn't already present (CR 701.27b).