By default, macOS doesn't allow applications to see what the user is pressing on their keyboard when the app isn't currently in use, and for good reason - a shady developer could make an app stores everything you type, which will almost certainly include some amount of sensitive information (i.e. passswords, credit cards, etc.).
Of course, most apps aren't doing that (or at least, one would hope), so you can also tell macOS to allow specific apps to "listen" to whatever keys you're typing.
One of Splitter's key features is the ability to control your run even if the app is in the background (a.k.a "Global Hotkeys"). This necessitates that Splitter be able to keep track of whatever you're typing (as long as the window is open), so you'll need to give it permission to do so.
I'd like to make it clear that Splitter does not keep a record of any key presses that you perform when you aren't using the app. In fact, the only time it keeps any record of what you press is when you record a custom hotkey - so you can, you know, record a custom hotkey. In this case, all that is recorded is the custom hotkey that you type. When you remove or override a custom hotkey with a new one, the previous value is completely removed from memory.
TL;DR: If you'd like to give Splitter permission to have Global Hotkeys, open System Preferences, search for "Privacy Settings", unlock the padlock, scroll to Accessibility, and click the check next to Splitter. You may also need to quit Splitter and reopen it in order for the change to take effect.
Of course, if you don't want to do that, you can still use the rest of Splitter's functionality. You can even still customize the hotkeys, too - but they won't activate unless Splitter is the currently active app.
If Splitter doesn't appear in the list in System Preferences, click the Splitter icon on the Dock to reveal it in Finder, then drag the app from Finder to the list.