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Totally normal and in some cases desired. When you are playing notes the open strings will ring out making sympathetic tones. I don’t remember off hand what key Tony plays Billy in the Low ground but let say it is G. When you hit the Bass note of G on the low E string the open string G will ring out sympathetically, activated by the vibration of the guitar itself. other strings will also ring out like the B string and the E. You can test this by just playing a single note loudly and slightly touching all the other strings to see which ones are vibrating. A light built highly active guitar will have lots of sympathetic tones. They should all be pleasing tones aligned with the key being played when tuned. If something is sounding wonky try retuning and playing again.
If the sympathetic tones are not what you want you will have to play in closed positions and get good at muting- barring with index as a damper.