'fraid so. The wobble is often an early symptom of the crank nose problem. I'd do some reading and then take it back to the workshop that did the timing belt change to discuss a proper diagnosis and a way forward.
Early MX5s, up to about '91, had what was called the "short nosed crank" or SNC. The nose at the front of the crank was not well enough designed to provide a strong mount for the crankshaft pulley. The crankshaft pulley is usually removed and re-fitted during a timing belt change. If the mechanic was sloppy or just unlucky in his work then some time later the pulley would start to work loose and wobble.
Mazda redesigned the crank nose for the later 1600s and for your NA8 - aka the "long nosed crank" or LNC. It's a fair bit better but still not perfect, so there are still instances of the problem on the LNC motors. The failure will turn up anytime from a few hundred kms up to thousands of kms after the timing belt job. On my NA8 it first appeared 40,000kms after the belt change and I didn't fix it (with a new crankshaft) until I had other engine problems after 75,000kms.
There's a lot of posts about diagnosing it and repairing it. Try googling "short nosed crank" on this site or on
http://www.miata.net.
Basically you've got a sympton of it. So there's some probability that you've got the LNC problem. If that's the case and the belt was changed 8,000km ago then there's a strong probability that you have the problem because the belt change was not done well enough.
