International Day Pass charges.

 Day pass

What do you mean you can't turn off Wi-Fi assist?  If you have an iPhone you absolutely can turn and should turn Wi-Fi assist off otherwise your phone will try to connect to Cellular. 

On your iphone, go to settings, scroll all the way to the bottom and Wi-Fi assist switch is at the bottom. Switch it to the off position.

You can also put your phone in airplane mode and leave it there.

Or turn your phone off. If your phone is connecting to a foreign cell phone tower and using service you are responsible for the charges. Not paying them will result in having your service turned off, losing your phone number and having a bad debt that'll follow you for decades.

other wise I will not be responsible for making payment for $10.00/day charges

 You're posting on a customer populated forum, if you think this is somehow notifying AT&T that you're not responsible, that's not going to work. 

You are responsible to control the phone. Turn it off if you don't know how to control it properly. It's not AT&T's responsibility to keep you from spending $10 a day because you don't know how to operate your phone

Just to review, if you are outside of the United States, International day pass only charges you $10 a day on days you use your phone to make or receive a phone call, send a text message, incoming text messages are free, or use data well they're actively or in the background on your phone. The alternate to the $10 per day charge would be pay per use charges which can be up to $4 per minute for phone calls 50 cents for regular text messages $1.30 for multimedia messages and $2.05 per megabyte for data usage

It’s under settings > cellular, near the bottom.