I see nothing weird about this. Bayern urgently needed more depth in their defense after they had gone into the season severely understaffed. Dier covers the CB, RB and DM positions, is so cheap he might as well have been free (and I doubt his wages are huge either), he still has enough years in him to have a resale value and he's probably very aware that unless he suddenly improves massively he'll only be the 4th pick behind Upamecano, Kim (at least as soon as he's back from his tournament) and de Ligt.
Bayern gets some urgently needed squad depth for peanuts, Dier can put himself into the window at a different club, Kane gets to hang out with a friend, Spurs still gets at least some money for a player that is surplus and almost out of contract - everybody wins. Looks like a sensible transfer to me.