There are many ways to express these ideas. Neither example you provide is wrong. Which of the many ways is best would depend on where you are and who you're speaking with. Frankly, it is more important to be clear than it is to be dialectically precise.
For example, I would express the idea as:
Usually Omar buys stamps on the morning of the first day of the month.
Note the differet prepositions. I'd probably start a fight if I suggested that "on" is more appropriate than "in" or vice-versa.
However, the "of" ("of the first...") is better than "on" because the morning belongs to a specific day and "of" is indicating that possessiveness.
It's also a habit to put the "smallest" aspect of an idea first. Thus "morning" comes before "day," which comes before "month", because each is in turn a part of the next item in line. I doubt it's an actual rule, but it does sound most natural to my ear.