EAGLE has no say over the outcome of the thickness of the actual copper layers themselves, since you'll be etching the board yourself and you're the one picking the copper board stock. However, you can increase the size of the annular ring to give yourself more room to drill a hole close to the center of a PTH.
Using the Info tool (the button that is the letter i), click on the PTH you are interested in and adjust the Diameter from auto to another value that is greater than your Drill size. Click Apply and visually inspect the hole - if it's still not as much copper as you want, increase the Diameter again until it's as thick as you want.
If you want to do this to all your PTHs, just use the Change tool, go to Diameter, and click the ... option at thebottom to set a custom value. This would ideally be the Diameter you chose when playing around with a single PTH. Then just start clicking on the other PTHs you want to update them.
This will only work, however, on PTHs you defined manually on the board layout. If some PTHs are part of the part's package, for example, you will have to edit their Diameter manually in the package itself, not in the board layout.
I would call SeeedStudio and talk to their manufacturing (or CAM) department. Different shops write their specs in different ways, and it's costly (in both time and money) to misinterpret what they're trying to say.
In the manufacturing process, first the hole is drilled, and then it is plated. The plating causes the finished hole size to be smaller than the drill size.
However, Advanced Circuits, for example, assumes that the hole size in your design documentation is what you would like your finished hole size to be. So, if your drill file has a 10-mil drill, what you get is a 10-mil finished hole. They automatically increase the drill size so that the finished hole size is what you specify.
(I am not affiliated with Advanced Circuits, but I have been very satisfied with their services)
So, give SeeedStudio a call (or an email) and see what they say :)
Best Answer
That is a recommendation of layout, not the size of the pin itself. In this case, the hole should still be 1.3mm.
If you look at the mechanical drawing of the part, it shows that the pin is 1.18mm wide, so 1.30mm clearly accounts for some margin.
If you are really unsure, you can ask you assembly house if such tolerance is enough for the placing machine. If you are placing by hand, you should be fine.
A different question is how your fab house interprets those hole dimensions (some interpret as finished dimensions, other as drill size), but this is a problem for plated holes mostly - not the case here.