If I equipped my follower in heavy armour when he/she is proficient in light armour, is that a disadvantage at all or is it still providing heavy armour protection?
Should I really only equip them in what they are good with?
Your follower will get heavy armor protection from heavy armor if you equip them with it, regardless of what their skills are. However, they won't be able to take full advantage of it like a heavy armor specialist would. And they would be missing out on the advantages their light armor specialty gives them. So the answer to your second question is "yes". In the vast majority of circumstances, you should equip your followers with the type of gear they're good at using.
Different followers have different uses. Lydia is a heavy armor specialist who makes a great tank, but she's lousy at sneaking. Marcurio has devastating offensive spells and moderate sneaking ability, but he svcks at hand-to-hand combat. Cicero is super sneaky and good with a dagger or bow, but he's lightly armored. Depending on your play style, any of these followers might be good for you or bad for you. For example, there's no use picking Cicero if you're clanking around in heavy armor, as his greatest strength (sneaking) will never come into play. Conversely, Lydia is a poor follower if you want to be sneaky, because she's loud and aggressive and will constantly blow your cover.
Decide what your play style is. Pick a follower whose skills compliment it, and equip them appropriately. Here is the http://www.uesp.net/wiki/Skyrim:Followers. It shows you what their primary skills are, so you know what they're good at and how to equip them.