I can't make out the meaning of the phrases
Here's a paragraph from the sutra named Advice to Venerable Punna.
Venerable Punna, delighting in the words of the Blessed One, got up from his seat, worshipped the Blessed One, and moving with his right side towards the Blessed One showed reverence. Putting his dwelling in order and taking bowl and robes, he left on a tour to Sunaparanta and arrived there in due order. Then he abode in that state. Venerable Punna, during that same rains, brought forth about five hundred male disciples and about five hundred female disciples and realized the three knowledge’s and venerable Punna attained final extinction.
Q1:What 'in due order' means here?
Q2:What 'that same rains' means here?Does it refer to the rain season?
I'm looking forward to your help.Thanks so much.