This is the first time I've heard them referred to as spiders, but I love it! Little glob of fabric holding on by a thread
When I first started sewing with garment construction, the seam allowance was so wide getting sucked down into the hole wasn't an issue, I was taught to hold on to the threads when I started, besides that meant they were to the back which is where they should be.
Now I use "leaders" all the time, pretty much every time, even when I am sewing wide seams or large pieces. I always have little scraps left from cutting anyway.
I recently saw a hint somewhere about precision piecing, it really helps if you have the correct markings on your sewing machine or draw the lines, but when you are doing a lot of triangles reverse every other piece. Hard for me to describe, but instead of your chain looking like >>> you go >< so the seam and pieces nest in a straight line.