当時私は母が入れ物に入れた餌を自分で動物たちに与えた
I would have expected the above sentence to use てい form (与えていた) as it seems like a repeated action in the past. The speaker is talking about their childhood chores, so I thought that it translated roughly as "At that time, I used to feed the animals myself with food that my mother put in a container."
I'm assuming the reason 与えた is used instead is the word 当時 (at that time). Is this correct? Are there any another common adverbs of time I should watch out for?
While your understanding of using テイル for repeated actions is not off,
the reason 与えた is used instead is the word 当時
is not exactly true.
It is more simply the writer's choice for the particular case. That is, 与えていた should work, too. Similarly, to some extent, I suppose all of I used to feed/fed/was feeding are basically ok in English.
Use of past/past progressive depends on multiple factors. I just give a few examples; I don't think there can be a comprehensive rule when to use which or when both are fine. In particular, no expression really enforces use of テイル. If any, it is the nature of the verb used.
当時私は漱石を読んでいた/読んだ - The former is simply progressive; the latter sounds like having finished reading.
子供のころ毎日この道を通った/通っていた - Both are the same to me.
そのころ私は問題を抱えていた - Only ていた is acceptable, due to the nature of 抱える (which sounds like an action of holding it).
