That is correct. In most events you will only play against players who were also in the Amateur tier when they entered the event. There are a few tournaments (Ready-Gos, the premium weekly multiround, the Open Qualifiers) where the format is tierless. In a tierless event everyone competes against every one else, but each player plays from his own tees.
Every so often there will be instances where some players who enter a tiered tournament as an Amateur will receive a promotion to the next tier during the competition. They will be listed as Pro on their profile, but since they entered the tourney as an Amateur they remain competing in that tier for the duration of the event. In cases like this the newly turned Pro will be able to finish out the tournament as an Amateur, but will only be allowed to use non-pro level clubs.