We use already to show that something has happened sooner than it was expected to happen. Like still, it comes before the main verb:
The car is OK. I’ve already fixed it. It was early but they were already sleeping.
… or after the present simple or past simple of the verb be:
It was early but we were already tired. We are already late.
Please, let the course creators do their job!
That wasn't really a solid argument for imposing unusual restrictions on common usage found in writing and speech. From a more academic standpoint, adverbs are found in many different positions syntactically in English. Some adverbs are restricted to certain positions while others are freer. The rules or rationale for the variations do not exist, unfortunately. I think you might be getting at a rule of thumb to sound safely acceptable for less certain speakers but it won't be what they necessarily encounter as listeners. This is known to be one of the most challenging (and ridiculous) aspects of learning English as a foreign language because there are inconsistent restrictions on a major word category that are easy to violate and native speaker usage per dialect (Midwest US speakers begin sentences with "anymore," while I would never use that, only "nowadays.") is the only thing defining the boundaries. Hopefully, total free variation of syntactic position will come up in future speaker generations as a sane solution.