When I got home today, I saw that 2 of the new shoots out of twelve of my jasmine looked like they'd been cut off near the soil. When I looked closer, I saw a little bug - i crushed it so quickly i dont remember much about it, other than it was small and a rusty colour. is this a red spider mite? i saw some bug killer at the store that said it would get rid of all types of mites, is it worth me doing this? if there was one, is there likely to be loads more? i have looked, both on the surface and on the plant and not seen anything.

if anyone can help, let me know

thanks all!