It probably depends on the type of LED strip you have.
Mine (the product I linked to in the original post) was enclosed in a transparent silicone rectangular “tube” for water protection, which gives it a slightly rubbery surface. Putting that kind LED strip into the acrylic tube was easy. I just wound it onto a support paper tube (a rolled up A3 sheet) with the diameter such that I could just slide it into the acrylic tube. Then, I taped one end of the strip to the acrylic tube, and by turning the paper tube, the LED strip winding got a bit wider and laid itself nicely to the inner wall of the acrylic tube. I pulled out the paper and taped the other end of the strip.
I can imagine that this would not work with bare WS2812 strips.