I've not looked at his figures but I read into the tweet that he was basing the allowance for inflation on how much Premier League income had increased over the period thanks to the crazy TV money, etc. coming into the game. That's going to be a much more pronounced difference than if one used a more general measure of inflation, hence our seemingly excessive adjusted spending.
According to this... https://www.inflationtool.com/british-pound/1998-to-present-value £6million in 1998 is £9.2million in 2020