Most likely your pipes need time to settle in, this normally requires 5-10 minutes of playing. Being a windblown instrument the reeds react to the slightest change in climatic conditions, particuraly excess moisture or extreme dryness and will require time to settle.
As a suggestion, initally 'roughly' tune your pipes, then after a few minutes fine tune them either by ear or using the HBT1 tuner.
If your pipes continue to vary and sound unstable check them with your tutor. Mostly likely it maybe a reed/bag problem and may require adjustment or replacement.