Hi,
There is nothing in the paypal pro plugin which can cause an issue on a specific browser.
The plugin read the credit card details and call Paypal pro ; depending the result the order is created or not.
If not, the user will stay in the checkout.
If the order is created the user will see the "thank you page" of Paypal pro (which can have a redirection to another page depending your configuration).
That process can't be influence by a browser ; there is no interaction between paypal pro and the browser.
The only advice that I can give you is to check that your template right display the Joomla message and to activate the "debug" mode in the plugin in order to store some trace in the HikaShop payment log file.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.