We have some Sylvania "Luxline Plus" 6 foot T8 colour-860 tubes in the office at work and in the morning when first switched on, they exhibit the same sort of behavior. This is usually most noticeable on a cold morning, probably the phosphor is cold so exaggerates the effect. Sometimes, strangely, there are two dim spots with the ends and the middle being brighter. It is probably the mercury content, I reckon it becomes unevenly distributed along the length as they cool down from the day before - the ends stay warmer for longer as they run hotter to begin with and there is more mass there retaining the heat too. As you point out, after a short while they warm up and run just fine, probably vaporises the condensed mercury back into the tube atmosphere.
Strangely, I never noticed this with the horrible "plain vanilla" 3500K colour tubes that were there originally. Perhaps those older tubes had more mercury in them. I do notice the Sylvania tubes claim to be "New Generation".