If the tube rotated to produce "gravity", that gravity would pull down to the outside of the tube. So people would look up at the suns passing by.
If the suns have the mass of Sol, the Sun, they will eventually swell into red giants and greatly increase their luminosity after about ten billion years. That will cook the inside of the cylinder and maybe evaporate it into gas escaping into space. Then the red giant stars would turn in to white dwarfs after shedding significant amounts of mass. The stellar mass loss would produced strong solar winds which might push apart the cylinder, destroying it and would certainly devastate the already devastated surface.
One way to avoid it would be to make the cylinder much narrower and make the suns correspondingly dimmer than the Sun to adjust for the closer distance to the surface of the cylinder. Those dimmer stars will have lower mass than the Sun and will have steady luminosity for a much longer length of time, hundreds of billions or maybe trillions of years depending on their mass.
Or the suns could be stars which were already white dwarfs and which would be very, very gradually dimming down to black dwarfs. That would also take a very long time, perhaps trillions of years.
Or maybe you could make the suns giant lamps moving down the cylinder. They would have giant fusion generators to generate the power for the giant lamps used to illuminate the inside surface of the cylinder.
Of course maybe you don't care abut whether your setting will last for one billion years, ten billion years, a hundred billion years, or a trillion years.
Have you thought about what material your world would be made out of? You might need some hyopthetical fictional super strong materials.
Have you read Larry Niven's article "Bigger than Worlds"?