Your first sentence is fine, assuming that the figuring out of the details will take into account events that occur after the plan is agreed to. If that is not the case (if the figuring out is simply being postponed, and no consideration of new information will be made), then it would be better simply to say:
Let's agree to the plan for now and figure out the details later.
To take an action retrospectively simply means to perform the action with regards to previous events, or with hindsight. The etymology is useful in understanding the word: it is a borrowing from Latin that literally means to look back. There's no reason the events in question have to have happened in the past at the time the word is used.
Grammatically, in your first sentence, retrospectively is an adverb modifying the verb figure out. The figuring out is happening in the future, and the retrospective aspect refers to events that will have happened before that time. (Even though most dictionary definitions use the word past, they mean in the past from the point of view of the verb that is being modified.)
I agree with Tashus that making the figure out explicitly in the future reduces an chance of misunderstanding. Adding the word later works, so would using the future tense:
Let's agree to the plan for now and we will figure out the details retrospectively.
With that said, I don't like the usage in the second sentence. The meaning is clear enough, but the future "doing the actual training" doesn't really involve hindsight. If I were writing that sentence, I would simply say:
Let's check "yes, I have completed the training" for now and do the actual training later.