I've never used tumblr before or since and, to be honest, I barely know how it works. I just go straight to ENTM's page and avoid everything else. I think that a new website is in the works for them, too.
As for how it works, it depends on which Cycle you do. They have ones for tumblr (which is their 'classic' format, even though they haven't always been on tumblr,) Youtube, and Instagram.
Instagram is their newest kind and it is the only one that allows editing pictures, reshades, and mods. The pictures are judged by a panel of past contestants and prominent members of the community (e.g. glamour bloggers, staff members of fan magazines, etc.) After the judges score each picture, the fans are allowed to vote via Instagram on the top two to decide who wins that round and the bottom two to see who gets to stay and who is eliminated. Last contestant left wins.
Youtube is also an elimination cycle. Lowest scoring model of each round is eliminated and highest scoring one gets immunity in the next round. Again, the last remaining contestant wins. Judges are the same but the fans only get to vote during the fan bring-back round where they can vote for any of the models eliminated earlier in the cycle to return for the last few rounds. All of the models have to submit their shots at the start of the competition (as opposed to round by round with the other two formats) so that they can be edited together into the videos. There is also voicework from both the models and judges involved.
Tumblr is the classic format and is not an elimination cycle. Models submit their pictures round by round and fans are allowed to vote each time, though their results count for a lower percentage than the judges. (In my cycle the judging has been so close that it's the fan votes who have decided the winners most of the rounds, so they still carry weight.) The winner is decided by the highest total score from the entire competition, not just the most wins. In all of the cycles the judges don't just score the pictures, they give reviews to explain their scores and to help the models improve in the coming rounds.
Mini monthly challenges are just one-offs that are decided solely by fan votes. The winner of the previous month picks the new theme/requirements for the new challenge and also wins their choice of a minion off of the Mog Station.
If you are curious about it, you're more than welcome to join the Discord! https://discord.gg/QruxQx
Obligatory Roe pic!