Hi, I am not very familiar with site-directed mutagenesis protocols. However the rationale behind using a DNA methylase in amplification could be to facilitate methylation of DNA thereby reducing the off target or non-specific effects. Not sure, just a guess!
This system using an E. coli strain expressing McrBC endonuclease which specifically recognizes and cleaves methylated DNA. As the lower efficiency of in vitro digestion, only the full methylated DNA will be completely digested. In this method, the methylase methylates your parent template before PCR amplification and after you transformed your PCR reaction into that E. coli strain, the McrBC endonuclease will digest the methylated parent plasmid DNA and left your PCR amplified mutant DNA (non-methylated) intact for replication. In that case, all the colonies you got should harbour the plasmid containing your mutation. If you think that your parent template is heavily methylated, the methylation step can be removed. If you use QiuickChange method which use DpnI to digest the methylated parent DNA more efficiently in vitro, you don't need the methylation step, any plasmid DNA purified from E. coli is methylated enough for DpnI digestion.
A modified QiuickChange protocol has proved very simple and efficient ( doi: 10.1186/1472-6750-8-91), you don't need any kit, normal proofreading thermal Pol and DpnI will do the job. The attached file is my lab protocol summarised form that publication which is much easier to follow. You can try it if you experienced difficulty by using GeneArt Site-Directed mutagenesis system.