The following is a quote from the Wikipedia website which has a great description about the sleep stages. Below it is a link to that website which gives much more information.
Click here for link to Wikipedia webpage
Sleep proceeds in cycles of REM and the four stages of NREM, the order normally being:
stages 1 > 2 > 3 > 4 > 3 > 2 > REM.
In humans this cycle is on average 90 to 110 minutes, with a greater amount of stages 3 and 4 early in the night and more REM later in the night.
I don't know all that much about sleep, but I don't think REM is necessarily the deepest stage of sleep, it's just different, in my opinion. And as the website says, "each phase may have a distinct physiological function." REM sleep is a small percentage of the overall sleep cycle, but that doesn't mean it's less important.
And yes, it would have been better if the sleep tech had let you finish the second REM. I don't know how long it took for you to fall asleep or how long you slept, but I'm guessing that would be a factor in how often you cycle through the different stages. Also, if you have sleep apnea, very likely your sleep stages are quite different. But yes, the data would have been better with more of the REM. But it's more important to complete as much of the REM episodes when being titrated, perhaps more important than the baseline study where they test you without cpap first. With titration, they need to know what pressure will stop the apneas in all stages. Still, it's important to know the nature of REM in the baseline, because some people have a higher AHI during REM (everyone's different).
But then again, sleep techs, who work 12 hour shifts, are anxious to get out of there in the morning and may be quick to get the patients up a little too early. As the Wikipedia says, more REM occurs later in the night or towards the end of the sleep period.
The most important thing is the overall data of your report... how bad is your apnea, your blood oxygen levels, etc.