^^^^^
Yep, that's the way it works. Look closely at what you are buying, it should be clearly documented.
Since you mentioned interest payments, one surprise I had recently was not getting interest payments "on time". Example: If you buy a one year CD that pays interest monthly, you "may not" receive your monthly interest payments on time as you might be expecting. I've had several interest payments post to my account several days late. Schwab tells me they won't post interest payments until they actually receive them from the issuing bank. Seems they have some sort of a grace period. Most have been paying on time but a few don't.
Too bad that doesn't work that way when I'm paying my bills.