Firstly, being registered and being active are different.
You can have registered customer who are not active in your system. Active for shall be used for the customer who are active in your system.
Being precise and relative are not the same thing.
Registration date can be shown absolute (DD/MM/YYYY) or relative (x +- 31 days/hours etc..). The other degree of the time Rounded or Precise here.
Any system would like to have active members and therefore "active for xx days" message promotes more traffic and towards positive behavioral change. In this case rounding toward up is better option.
Let's think about the punishment of criminal or ban from a game. The punishment itself shall be more precise and rounding up is not good going to be fairness. You can not say 345 days as 11 months. You need to be more precise for the system itself.
As in your question, rounding up registration date is related to your system itself. For instance, If there is monthly payment involved, you should be more precise, in my opinion.
Last but not the least, the purpose of this message is the key of your decision. Why do you put this date will lead you a rational way.