Once I'm logged in on your checkout, I don't see the taxes but I see them before being logged in. That means that the problem is that your tax rules are not configured properly and do not tax my address, that's all. And it's normal that you don't see the taxes in paypal and in the email/order, since you don't even see them on the checkout once you enter your address.
I went on your back end to look at your tax setup. You have two texas states in your zones. The zones with the id 4000 and 4307.
The one you set in your tax rule is the zone 4000. However, the one you have attached as a subzone in the USA country zone is 4307. So that means that your customers will select the 4307 one while the tax will only be applied with the address is in the zone 4000, which is not possible since that zone cannot be selected.
So you just have to edit your tax rule and change the zone to the 4307 one and it will work: taxes will be applied for customers with an address in texas.