Q: Faulty or incorrect battery meter on iPhone 6S

Chummie,

Return it for warranty/exchange service.

This may be unrelated to your problem, but there is a known bug regarding the battery meter on the 6S.

http://www.cbsnews.com/news/apple-admits-bug-in-iphone-6s-battery-meter/

I have noticed a similar issue with my 6s. What happens to me is that I'll plug my phone in, leave it alone for awhile, and the percentage will seem to have barely changed, and then I'll set it down for about two minutes and the percentage will have increased significantly and is at where I expected it to be. It seems to me like this isn't something to worry about too much.

Check this Apple support document that addresses questions about the battery percentage and the iPhone 6s series. If your iPhone 6s or iPhone 6s Plus battery percentage doesn't update - Apple Support

Thanks for the link. I'm wondering if you can avoid the problem by turning "set automatically" off before you travel to a different time zone.

That I couldn't tell you. All I am aware of is what is listed in the support document.