This would depend on the version of Jump Desktop that you have purchased.
If for example you have purchased Jump Desktop for iOS, you don't have to pay again if you want to install Jump on your other iPad, iPhone or iPod Touch.
Similarly, if you have purchased Jump Desktop for Mac, you can use it on all your Macs to connect from Mac to Mac or Mac to PC.
If however you have purchased Jump Desktop for iOS and now want to connect from your Mac, you will additionally need to purchase Jump Desktop for Mac in order to get this connectivity.
Please make sure to use the same iTunes account from which you initially made your purchase when installing Jump Desktop on subsequent machines or devices.
How to Re-Install Jump Desktop or Install it on subsequent devices or machines:
Lets say you've already purchased the desired version of Jump Desktop and now want to install it on a subsequent iOS device or Mac: Open up the App Store app and re-purchase Jump. This is important: Make sure you use the same iTunes account you used to purchase Jump Desktop earlier. After the purchase is complete you'll be shown an alert telling you that you've already purchased the app earlier and that the download will be free.
Note: You can use the above method if you delete Jump from your device and want to reinstall it.