My DM insists on the combat being 10 seconds per turn and the round time to be the sum of all turn times (so a minute for 6 participants, for example). I am aware that this is not how turn/round time normally works.

This makes many spells with 1 minute durations like Hold Monster last at most a round.

I am playing a Fiend Warlock and I am worried it'll seriously underpower my character compared to non-spellcasters. Many spells available to me are supposed to last up to encounter-long (Hold Monster, Hunger of Hadar, Vampiric Touch, Hold Monster, Eyebite to name a few). Am I rightly worried, or overreacting? Are other spells sufficient for me to carry my weight?

I am aware of PHB's ruling on this and that rounds normally don't sum to turns. I brought it up in the conversation with my DM but it's his idea and he said that it has to be this way or the campaign's BBEG would be too strong. To me it sounds like a problem with balancing the BBEG and breaking other things is not the way but I wanted a second opinion on how this affects the game.