He's a good manager and someone who definitely will be around the top of every big clubs' shortlist if they change managers, but if he is to stay at Spurs, he needs to start winning something- LC, FA Cup, it doesn't matter.
He was lucky that there was an air of negativity around the club for no apparent reason when he joined (they were 5th IIRC when they sacked AVB, behind an in-form Arsenal side, Luis Suarez driven Pool, Chelsea under Mou and a City side who are backed by a country's government), and so winning over fans was pretty easy for him. But, the excuse that "we aren't rich like Utd or City"/ "we shouldn't even be this high, be grateful" argument can not stand for a lot more years. They have a great starting XI and should focus on keeping these players for as long as they can and get in some good squad players as well.
Additionally, what has worked in his favour and went against Koeman at Everton, AVB at Spurs, etc. has been that he hasn't had a transfer window where he has spent a lot of cash. Once, he does that, the relationship with board changes, the expectations change and should the signings not work out, you are a dead man. It would be interesting how he rebuilds this Spurs side if he does stay for that long