There very well could be a short in the RTA itself, but I would find that to be unlikely. More likely is your coils shorted out because they touched another metal part of the atomizer base - there wasn't much room between the coils and the posts or the base floor and could have arc'd.
When you "pulse" your coils, they should only be pulsed long enough for them to begin to glow orange. The glow should start at the very middle of the coil and spread outward. If a "leg or arm" of the coil, or if the "end" of the coil glows first instead, then there is either a short or the coil is not balanced.
I would discard the coils that got burnt and start out new. Since you are new to making your own coils, play it safe and target a coil resistance of 2 ohms if using two coils (together results in 1 ohm), or 1 ohm if using one coil. With a regulated mod, you can always crank up the power to get a decent vape even with higher resistance coils. With low resistance coils (sub-ohm) you have a much smaller margin for error for creating a bad situation.
The first blog below was designed primarily for mechanical mods, but the middle portion that goes into
coil building is sound for
both mechanical and regulated mods. Learn to use a coil winding calculator like Steam Engine as shown in the blog. There's a tutorial video on making a simple coil, too.