TinyUmbrella 6.13.00 supports iOS 6.1.3 and the relevant devices. I've also fixed a nagging bug that windows users have reported (ClassNotFoundException on Platform). Thank you all for your support and feedback!
We definitely recommend following our Mac or Windows tutorial on how to save your SHSH blobs using TinyUmbrella. More information about SHSH Blobs and AP Tickets see Saurik's detailed explanation.