Does Random Seed affects my models after trained/exported

I am in great doubt about one of my models. I've trained a Random Forest model and found the best parameters after a grid search, however i forgot to set at seed at the moment.

Once I had my best model, I exported these parameters to be able to reproduced my results.

I have a set of data that once labelled by my best model it gets X probability. However, I ran the same set of data again through the same model and got a diferent probability.

Does the random seed impacts in any way my trained model in this case? I MUST set a random seed when exporting my parameters?