Auxiliaries stayed outside naval treaty tonnage

Did fleet supply trains fall under the naval treaties?

No. Auxiliary supply ships were kept outside the treaty tonnage limits.

A short answer establishes an important boundary in treaty-era fleet design. Oilers and other auxiliaries did not consume the tonnage allowances assigned to battleships, cruisers, destroyers, or submarines. Navies could therefore expand support capacity without trading away a treaty-limited combatant. Industrial capacity and budgets still constrained construction even when the diplomatic agreements did not.