You need consider scribing process.
This is no drilling, this is simple cutting board by disk cutter on 2/3 depth (or more, or less, as you will ask manufacture) from both side. Scribing cheap and should be FOC for you.
Both scribing and drilling used for preparing boards for next separation after assembling.
For reflow soldering multiple boards still joined together on one big plate after PCB production process but prepared for separation.
Drilling used only for board with difficult geometry (not square boards). All PCB boards should be already processed by cutters and only small bridges between multiple boards must be present and drilled.
This is far away from that your received from your Chinese partners. When your sub-boards will be separated by breaking, you will need to do mechanical processing for each side of your sub-boards. Or you will be have inaccurate sub-boards with sharp peaks after breaking.
With scribing you will be have much better results, and no any drilling! between sub-boards. Your business card will be still look as one unit, but will be prepared for separating.
