We ____________ on the next actions to take before engaging them.
You indicated that the simple past seems correct to you because the time marker at the end of the model sentence is in the past. Based on this sentence alone, I have no reason to agree with you.
We will decide on the next actions to take before engaging them.
The phrase "before engaging them" has no tense. It has a non-finite verb form. Even though we traditionally call this form the present participle, it doesn't indicate either the present or the past. It indicates the active voice and the continuous aspect, but it's placement in time could be anywhere in the past, present or future.
The two options under consideration imply that "engaging them" lies in the future:
1) We have been deciding on the next actions to take before engaging them.
2) We have decided on the next actions to take before engaging them.
In the absence of further context, both options are sound and sensible. The action of deciding began in the past. In the first option, that action continues. It began in the past, continues now, and is expected to end in the future. In the second, it does not continue. The action began in the past, ended in the past, and its results exist in the present.
One important phrase in the paragraph above is "in the absence of further context". Chances are very good that both you and your tutor have further context. It's also likely that you don't have the same context, or at least you don't have the same understanding of the context involved.
What you want to know is why your tutor assumes that the action of deciding is complete. The model sentence on its own doesn't provide that essential context. You'll need your tutor to explain why she assumes that the decision-making process has ended.
It is possible that your tutor is teaching from incomplete or incorrect materials. If the publisher of these exercises failed to provide enough context to make its answer key sensible, then there's nothing that you, your tutor, or any of us reading your question can do about that mistake.
If "engaging them" does indeed lie in the past (as you initially suggested) then the most obvious perfect-aspect fit for the blank would be a past perfect construction:
We had decided on the next actions to take before engaging them.