The Milky Way is 100,000 ly across, so traveling at 1/10 the speed of light that’s 1 million years not 650,000. Plus of course there’s the assumption of no “distractions” which doesn’t really hold water. Plus of course even if somebody went across who says they come to here. And colonization takes a lot longer than merely travel. And we don’t know when they started, if they started on this 1 million year journey 750,000 years ago they’re “almost” here... and we won’t encounter them for many times our recorded history.
Actually it would take much longer because you can not travel through the center of the galaxy.
That means that star travelers will have to travel along the rim to reach us.