I don’t think that my pH would change unless I were to drink the liquid medium itself, so my answer has to be, “No, it is not normal for [one’s] pH to go up while cycling a tank.”
It would also be helpful to explain what you mean by “pH go up”. Do you mean to become “more base” (which is what is represented by an increasing pH value), or to become “more acid” (which is what non-chemists colloquially mean, I think, when they talk about “higher pH”, since lay people don’t often get that “strong bases” can be as damaging in their way as “strong acids”).
The previous respondents to this question are obviously not so confused, but later visitors to this question may be. Also, those who don’t understand that by “a tank” you mean “an aquarium”.
You’re welcome.