I also have not played many of the mentioned games or tabletops, but did dable in some D&D. And I don't know how the OP played it, but for me it was always "heroes act", "opponents act". Sure, we could choose amongst ourselves which of us went first, second etc. but like X-Com it's not the same as here where a turn isn't one side's actions, and the next turn another, but one turn rules everyone.
What kind of crazy D&D gaming is that?
Usually a DM makes one initiative check for the monsters, but 1) he can split them into individual checks for the monsters if he wants and 2) depending on how he rolls those monsters turn can end up anywhere between the individual player's turn for that round.
So, you can end up with a turn order that looks like this: Warrior Jane, Rogue Jack, Cleric Bob, 15 orcs, Wizard Tom
It's pretty much just like how Divinity : OS combat turns play out.
Of course, DM's can do whatever they want, so if yours always did players first and then monsters, then that must have been his preference.