Cache should speed up your website not slowing them down (((: very strange support I thing who told somethign like that, support mostly proposing enable the cache on the website ...
Anyway, I dont know what website do you have is it a CMS like wordpress or different solution, if Wordpress the first steps you should take is to find a plugin called AutoOptimize, its doing a lot of things to speed up your website, lets say if your website loads 6 seconds it can reduce that time even to 3 seconds without doing anything except installing of those plugin and configure them. Of course there are many more ways of optimize your website to speed them up but it needs some coding someties so it may not be cheap way.