First, bamboo are really difficult to ID. I don't think I could do it from what you have. It does, however look like true bamboo, a grass that is 'woody' and does not die back to the ground. Lots of other plants are called bamboo and are not a grass at all, though I don't really argue with common names.
Ebay is notorious for having listings that are inaccurate with plants. Anybody can list, and they can have various backgrounds, not necessarily in horticulture or Botany. I do however get plants off Ebay and they are often unavailable from anywhere else. Some have really good info, better then nurseries, from people with real experience growing them day to day. It looks like you got a nice plant out of it.
Further, bamboo seeds are nearly never produced. This is probably not important to your situation as I think you did get real bamboo seeds ... They may not produce offspring exactly like the parent (that's how we get the multitude of cultivars - cultivated varieties of bamboo). They may also look quite different when young. It's also possible the lister just put up a generic photo of bamboo and has nothing to do with what you got. This is often stated somewhere in small of hard-to-find text.
As far as growth. It looks like you are doing what you need to do. Bamboo will droop. In the 'wild' some species grow together when young, supporting each other, but droop quite a bit on the margins. You just need to support them till the stems harden. Eventually your bamboo will send up lots of shoots and should be sort of self supporting, though those on the edge of the pot may still droop, but this can look quite nice.
Bamboo like abundant nutrients, especially nitrogen. But if you fertilize, it's hard to have the plant show nutrient deficiencies. Just remember to add nutrients as they mature. It might also help to re-pot them occasionally. They re-pot really easily and this can revitalize them too. I 'recycle' the old soil into new by composting it. Don't ever use it for seedlings, however.
When a few more years old, your bamboo may be identifiable. Or maybe someone out there has an idea. There simply is not enough for me to put through a key.