I take test cyp for my trt. The doctor always makes sure the bloods are 7 days after shot. That just keeps things consistent for measuring total test levels. They know it will be higher a few days earlier. But 7 days later usually eliminates the peaks and gives you what you lower test number would be for the week. So they adjust your dose to get it to the target number 7 days after shot because they don't want your total test to drop below that number. You also get another shot typically, at least I do a shot every week.
As to him testing after you have only been on 1 week that seems a waste. Not sure why he is doing that. You should be on it for at least 6 weeks before he tries to adjust your dose. Hope your not paying for the blood test.
It should be higher than before your shot, however it takes 4-7 weeks for your test levels to reach peak for a given dose of test cyp. Plus just starting on trt in a few weeks your body is going to shut down its on test so your number will drop at some point.