I had exactly the same experience when I first got my Tek light, I even called the manufacturer, feeling like an idiot. They sort of laugh at me.
In short, you have to press a bit harder. I believe the sockets are spring loaded and take a bit more force then any other t5 fixture I have ever used.
The good news, I have not broken a single bulb, even with my 2 left hands

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Push in and turn.
v3