These days it won't be a transformer but a small buck/boost converter or an SMPS.
A lot of the small LED strip controllers (the kind in heat shrink) will often work over the voltage range 5-24v but won't alter the voltage. It's simple enough to get the low current 5v the microcontroller needs and the dimming is done by PWM and over that range doesn't care about voltage.
If you do get a converter try not to buy on price. Most of the advertised current capacity is for ideal conditions fully heatsinked from the driver chip datasheet. It's unlikely to get anywhere near that without failing or getting very hot and many designs it's impossible to actually heatsink. Aim to overspec your current rating and test on the bench first - comfortably warm like a winter handwarmer is fine, any hotter avoid.
If you want reliability then look out for Pololu branded as these are well respected in the robotics/RC modelling community. Not as cheap but if installing it's what I'd use. You might recognise the modules as they are often cloned, some of the clones from eBay can be very good, some are terrible, you never know what grade of components have been used as they all look the same on the outside.