Assuming I understand your question correctly, it sounds like your booting your Mac to start up from macOS Recovery over the Internet.
If this is what's happening, then your most likely pressing the Option Command R keys during bootup (instead of just CommandR).
If you're absolutely sure that you're only pressing the Command R keys, then perhaps try using the Command key on the other side of the keyboard (in case you've got a problem with your keys).
By the way, the full process to disable SIP is:
- Start your computer
- Immediately hold down the commandR keys to boot into
- Click the Utilities menu and select Terminal
csrutil disable and press return
- Close the Terminal app
- Select Restart.... from the menu
Let me know if this helps or if you're still having problems doing this.