There's no rules here - you do what you need to do to get the result you want. In a well designed instrument, the snare beds should take care of excessive wire buzz - that's their primary purpose. Slackening the lugs either side of the wires effectively increases the depth of the snare bed, and that can sometimes decrease sympathetic buzz, but not always.
On a general note, sympathetic buzz is part of the package. It's often what gives the instrument some life in it's delivery. It's only when that buzz becomes excessive that measures need to be taken, & that's mostly in some of the more examining studio applications.
Sounds like a drum on youtube have a wealth on information on this subject. Their very first video is a snare drum tuning guide and they expand on tuning and methods over many videos. I've really found it helpful.