I don’t see why the grammatical cases of Latin and German matter in the interpretation of these abbreviations.

The Latin prepositions cum (with) and sine (without) are always followed by the ablative case. German has grammatical cases too, but no ablative. The German propositions mit (with) and ohne (without) are followed by the accusative case.

So c.t. = cum tempore = mit Zeit = with time (or with some delay), and s.t. = sine tempore = ohne Zeit = without time (or without delay).