Why is it grammatically correct to use the past perfect tense and then the past progressive tense?

The tense used for the verb "to pour" does not matter, as long as it is a tense of the past; this is so because the past perfect is used for actions that happened before another action that happens in the past (ref.). So the following would also be correct.

• My attorney had taken his shirt off and he poured beer on his chest, to facilitate the tanning process.

The past perfect is a sort of double past tense. The pouring of beer on his chest was preceded by his taking off his shirt.

The point of time the sentence is concerned with is that when he was pouring beer on his chest. The taking off of the shirt occurred at some previous, unspecified time.

Were the sentence to read My attorney took off his shirt and poured beer on his chest it would be a series of events where and would mark order and not coordination.

Note what happens when we reverse the order:

My attorney was pouring beer on his chest and had taken off his shirt

vs

My attorney was pouring beer on his chest and took off his shirt.