When using my Tamron 16-300mm lens I frequently experience chromatic aberrations in my photos. how so I prevent this?
You can't, really, unless you want to change to a better lens (they'll have that too, to some amount, but probably less obvious). Super zoom lenses like the 16-300 do always have various optical problems, a trade-off you'll have to take for the long zoom range.
The good news: chromatic aberrations are really easy to correct in post processing, if you shoot in RAW: good post processing applications, like Lightroom, will offer simple one-click removal of CA, LR even gives you automatic profile based correction of other problems, like distortion and vignetting, provided a profile for your lens exists, or you can even create one yourself.
Chromatic Aberration is one of major aberrations that thwart us from making a faithful image. Violet light has the shortest wave length thus it is the most refractable, it comes to a focus nearest the lens. Red with its longer wave length comes to a focus furthest downstream. Orange, yellow, green and blue focus in-between In other words, each color has its own unique focal length. Now image size is a function of focal length thus the red image is the larger and the violet image is the smallest. What we get is superimposed images each a different size and color. This shows itself as a fringe of color with the red image rimming this cluster of images.
The lens maker can mitigate but not eliminate. This aberration (color fringing) will be most obvious when you zoom to achieve higher magnification. Your only resort is to use high end editing software. PhotoShop and others feature routines that mitigate Chromatic Aberration and others as well.