Rest betweem sets doesn't pertain to time under tension, as that is only applicable while moving the weight.
Rest between sets is overrated IMO. While, I give people a general guideline of how long to take, in the grand scheme of things it's not an exact science.
Granted, I wouldn't want someone taking a 10 min chat session between sets. During endurance training they'll take shorter rest periods, during strength phases, longer rest periods.
You'll also find that rest periods between large muscle group exercises will need to be longer than say a bicep curl.
I'm sure others will chime in with varying opinions.