I'm not ignoring a thing, they weren't challenging that's a fact, you can't give him credit for challenging and then claim that they weren't actually challenging because there were mammoth teams during that time.
As for net spendings this is probably my favorite argument. They achieved that net spending by selling flops, bench players and castoffs that weren't playing for good money, during Pochettino's tenure the only starter that they sold was Walker. On paper Tottenham had the 3rd to 5th best team in the league every seasons and they didn't lose starters while still spending money on the transfer market(outside of one summer).
Just an example of the players they sold to achieve that net spend, these are the players after Walker in terms of fee. Wimmer, Chadli, Mason, Townsend, Soldado, Bentaleb, Paulinho, Sigurdsson, Pritchard, etc. Tottenham recouped around 230 millions out of these players that were unwanted and then you have 52 more millions for Walker.
In reality Tottenham spent money, found good players, kept them and sold a lot of dross for good money. I would say that it's fair to applaud Pochettino for helping many of these players achieve their potentials but it's not accurate to act as if Tottenham didn't spend money, I made that point in an other thread but Pochettino had more money to spend than Simeone but he did worse and while I already know that some will claim that La Liga is easier, good luck explaining Tottenham's EL performances.