I put money in a safe.
I’ve never seen “getan” used to mean “put”. This looks like “I done money in a safe”, which would be very odd in English. You could maybe say “I done put some money in a safe”, but that would be VERY informal English.
You are right.
It would be better to say : “Ich habe Geld in einen Safe gelegt.”
It is quite common to use “tun” in sentences, where other verbs would be appropriate.
However, when I did that as a child, my parents and teachers used to say:
“Tuten tut nur die Feuerwehr.”
(Untranslatable, literally “only the fire brigade does (= makes the sound) “toot”” but meaning “Don’t use “tun” in sentences, where it does not belong.” It is a play with the wrong use of “tut” and the similarity of “tuten” and “tun”.)
As in other cases, today’s parents might be less strict.