You probably didn't lean into the turn ^ it makes all the difference.
If you stay in your normal upright riding position while turning on a Spyder, you definitely feel like it wants to throw you off. You have to lean and slide your butt around, moreso than on a motorcycle.
This is easy to understand, and easy to do when you can see everything coming. I rode three different models at TMP a couple of years ago, and they are a blast (and you CAN lift a front wheel, no matter what the stability control is supposed to do

However, if you aren't planning your movements in advance, it's an entirely different story. One of the things we expect to have trouble with when moving from two wheels to 3 (trike, spyder, sidecar) is the steering. Since you still sit astride it, and operate it with handlebars, there's usually a concern that if you react to something, you may revert to push/counter steering and steer the wrong way, if only temporarily. For me, the bigger issue with the spyder was the fact that a simple tweak on the bars at speed results in a perfectly smooth, accurate swerve. Lots of stability, and knife-like precision, and it happens RIGHT NOW.
Riding around the track, executing turns or curves, it's a ton of fun. But if riding along on the street and you need to swerve suddenly, there's not always time to lean and slide your butt around, so you have to just squeeze as your swerve and hope. Now compound that with a passenger who may be even less prepared for the swerve.
I think I get the appeal for some people, but that alone made me wish I was sitting IN a seat, not astride one.