It's all about the geometry of the tip. For starter, T15 don't have that much thermal mass as they are mostly hollow. When a tip's thin, it lacks contact surface to transfer energy to the PCB and if it's long, it will also be much less sensitive to temperature changes (ie: PID loop can't sens and compensate heat loss). Just look at a fine long tip with a thermal imager, you'll see the wet tip isn't where the heat concentrates.
So, should you crank up the heat? Well, first I'd check that the long cartridge is actually calibrated at the part that's in contact with the PCB. That can be an issue for stations that don't offer per tip profile but you can't do much about it... Anyway, once you ensured that your tip gets you the temperature you set but it's still not quite enough to melt solder, you can crank it up within reason. If you have to go over 400°C, you're simply using the wrong tool and you'll just damage it or whatever you're working on. You need a preheater or/and a soldering station that's actually designed for sub-millimeter microsoldering (like popular JBC's C115 or C210 lineups). T15 is more for general purpose soldering like THT and mid size SMD.
Also, you shouldn't use tip tinner unless you've burned your tip and it doesn't wet anymore. It contains cleaning acid that's too aggressive for regular use.