I had the same problem but it turned out that the standard VM Invoice is not compatible with VM3. You need VM Invoice 3, which is a separate product.
See here:
www.artio.net/e-shop/virtuemart-tools
...there are two versions. I had recently renewed VM Invoice 2.5 when waiting on the VM Invoice 3 release so was not very happy, but Artio gave me a discount on 3. It seems to work file, a part from one minor bug....I don't know if this has been fixed yet though.
EDIT: Actually, having read your post again, I think the bug I get with VM Invoice 3 on J3.3 and VM3 is same as you report above. VM Invoice 2.5 would not work at all for me.....PDF invoices would not get created correctly.