Permanent makeup eyebrows darkening over time?

This should not be a major problem because most every permanent eyebrow tattooing will fade over time. It still may be different than the hair on your head but will lighten over time, so if this is something you want to do, I think you will be fine.

Typically with permanent cosmetics, pigments are used in the skin instead of ink which leads to a
slow fading process over time so that you will not have to worry about darkening of
pigmentation over the years. The pigments that are used are not the same that are used
in a regular tattooing process. Touch ups are sometimes necessary to
maintain the vibrancy of the pigment so you should not have any trouble with
your brows darkening as you age. A highly skilled permanent makeup artist will be able to blend color appropriately if you decide to touch up down the road to match your changing hair color.

Permanent makeup on the face typically fades with time.  You can also ask the provider to use a lighter pigment and then have them retouched more frequently if you are worried about any darkening.