As you mentioned, the rule in 8 ball is that the cue ball must contact an object ball from your own group first. There is no exception to this rule.
Hitting an opponent's ball and your ball at the exact same time is not the most common occurrence, but it can happen. This is called a "split shot" or a "split hit" with balls from opposing groups, and is a foul according to 8 ball rules.
When your cue ball hits a solid and a stripe at the exact same time, it doesn't matter that you called the shot that way. It makes no difference how you called it.
But yes, in some rare instances, you may strike your object ball and an opponent's object ball at the same time. In most cases, you as the shooter will be given the benefit of the doubt and the shot will be called legal.
So if you sink your opponent’s ball after hitting both balls at once, it will not be counted as a foul, but your turn (your inning) ends unless you also sunk your own ball into the called pocket. Regardless, all pocketed balls remain in the pockets.
If the match is presided over by a referee, and they observe that the cue ball hit the opponent's ball slightly before your own object ball, then it's a foul for you.
Generally, it's best to avoid shots like these where possible.