Montana does not require a money transmitter license, so if I register a company there am I exempt from money transmitter licenses?
You may be exempt from money transmitter licenses only in the state of Montana. Because you have an exemption in the state of Montana, does not mean that you can offer your financial services nationwide. The exemption is only valid for the state of Montana and Montana alone. This means that the transaction must originate within the state and terminate within the state of Montana. It cannot traverse or transit outside the state of Montana without additional licensing.
Unless your business is absolutely restricted to the state of Montana, you would require a money transmitter licenses in the other US states where your customers may be.