Tromell, Seymour's Butler

The value of X is determined only once, as Tromell's last ability resolves. To determine that value, look at the nontoken creatures you control and count each one that entered this turn. It doesn't matter if they were creatures when they entered or who controlled them when they entered.

While proliferating multiple times, players can't respond between proliferating the first time and proliferating the second time, and so on.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.