The Greek forward scored twice during an international window which ends on Saturday when Albion visit Bournemouth (3pm).
His two goals came for the club’s under-21s in a friendly against a PFA XI to add to his double against Oxford United in the Carabao Cup.
Compatriot Charalampos Kostoulas also played in both games as he too works towards a Prem chance.
Both have had to bide their time but Tzimas said: “They take care of us very much, the way they work on us to prepare us. They don't want to burn us.
“Because they also know the difficulties of a transition from this level we were, to the Premier League, where things are completely different.
“In general, so far we have a very good treatment.”
The departure of Matt O’Riley on loan to Marseille since Albion’s most recent game, against Manchester City, could open a gap for an attacking player on the bench as the Seagulls visit the Vitality Stadium.
Fabian Hurzeler will give a squad update from the training ground on Friday morning.
He has made it clear he is taking things “step by step” with his two Greek forwards, who have both been appreciative of their new environment.
Speaking to gazzetta.gr, Tzimas said: “It helps that we have such experienced players in the team, so whatever we need is there to ask for advice on any concerns we have.
“Football is not only physical, it is also mental. You have to be very strong mentally to manage all this.”