I can't quite figure out or find where it says when a pet hits the Adult stage. Does anyone know how many days?

Hey!

On a pets profile page (e.g. this one) you'll find a section as follows and I've highlighted the maturity in red:

Information
Name: Un-named
Pet ID: 1760757
Current Owner: Wander
Original Owner: Wander
Birthday: 09-08-2015 10:27:21PM
Age: 25 Days
Maturity: Adolescent
Profile Views: 7
Battle Record: 0-0 (0.00%)
Missions Completed: 0

Pets reach adulthood somewhere around the 26 - 28 day mark depending on how much they've been nurtured (it speeds it up) and how much downtime there's been (site downtime pauses the pet's aging).

If the pet has been genetically tested, you can also have a look at its image URL which will show how many hours old the pet is, like so:

https://www.sylestia.com/image_builder_pet.php?species=ny'vene&breed=sylesti&gender=female&gd1=NF&gd2=NN&gd3=NA&md1=NN&md2=NN&md3=NC&ec=f8fa1d&c1=164407&c2=f0f5a2&c3=0d5b0e&gd1c=83b546&gd2c=0f2505&gd3c=f6fb73&md1c=1c6a20&md2c=106819&md3c=faf76c&maturity=627&owned=1&size=500

Once the maturity number in the pet's image URL reaches 648 hours, it will be an adult.

(If the pet hasn't been genetically tested, the number will remain at the age the pet became an adolescent - 216 - until it actually reached adulthood at which time it will switch to the 648).