You've partially identified the problem, as you implied your starter isn't old enough. Plus the commercial yeast you used to start the culture is still sufficiently dominant that it controls.
Sourdough yeasts are not the same breeds as commercial. The commercial are chosen for their storage and reliability qualities as well as their light flavors. Sourdough yeasts are wild, usually endemic to a specific area.
For the "tang," you want you either have to obtain a starter of known quality or keep a levain going long enough for wild yeast to take over the culture. One of the best starters is "Carl's Oregon Trail" which you can get on the internet for the cost of sending an SASE to Friends of Carl. (Google them).
There are alternatives. One is to do just what you've been doing, but keep the levain going for at least two weeks at room temperature before expecting something closer to sourdough than pain au poolish. This is enough time for your indigenous wild yeast to take over the culture, or enough stress to select the heartiest, most sour spores from the commercial yeast (unnatural selection). But you won't have a really good idea of your starter's ultimate quality for a couple more months at least.
Another way, better calculated to get those wild spores, is to make a paste of 1/2 cup water, and 1/2 cup rye or whole wheat flour and add a few grapes to it, or a piece or two of cut fruit. Feed the next day with the same mix of water and flour, and stir. Let it sit out for two more days until it shows signs of life (bubbles, produces hootch, and/or expands) or the fruit begins to smell. Discard the fruit, and feed again with the same amounts of water and flour. Let it sit, stirring daily, until it again shows signs of life. Discard all but a cup and feed every other day -- discarding excess as you go in order to keep the total quantity manageable. Once you know the colony is active, you can switch to white flour. Some people add a little sugar now and then to keep the colony vigorous, but in my experience pampered yeast don't develop the great tang you're seeking. It doesn't matter how slow it is, taste trumps.
Again, you're going for a colony you can keep stable for two weeks, feeding every two or three days. And again, the individual character of the colony will continue to develop over several months -- or even a year. The thing about wild spores though, is you don't know what you're getting until you bake. I've had great cultures everywhere in SoCal except for where I live now. Oh, well.
(You probably already know this, but it bears saying for novices, that once the starter is well established (couple o' weeks) you can store in the refrigerator, and hold off feeding until the day before bake day.)
Once you've got a good starter going -- it's likely that your local yeast will eventually overtake whatever you spores you used in the beginning. That's the nature of leaving things out on the counter. It's also why people (accurately) compare starters to half-domesticated pets.
Hope this helps,