I've started learning Any% Glitchless a few days ago and can now quite consistendly get both the Nido manip and Paras manip on Gambatte-speedrun. But I also own a GBC with a cardridge of Red on which I get a lv 2 Rattata a few tiles earlier every time, what is causing this?

What causes this is RNG not working the same way on GBC and Gambatte-Speedrun. Gambatte-Speedrun has the GBA/GBP RNG, which the manips we have are made to work with.

So if I plug the same cardridge into a GBA I will be able to do the manips?

Yes