The Short Answer
The name you list does correspond to the first compound shown under the naming scheme you were given for the second compound, however last I checked the IUPAC scheme recommends "N,N-dimethyl-2-propanamine" not "N,N-dimethylamine-2-propane" if you want to be really strict about it.
A More Realistic Look at Naming
Putting all that aside, you'll not often see simple substituted amines referred to this way by chemists. IUPAC naming in general is useful for unambiguously naming large, tricky compounds but for smaller garden-variety ones it's often seen as unnecessarily cumbersome.
The IUPAC scheme names amines in reference to the longest carbon chain (e.g. "N,N-dimethyl-2-propanamine"). The more common scheme for amines with relatively simple substituents is to name them in reference to the amine group instead (e.g. "dimethyl isopropyl amine").
This is similar to the common-name schemes for most other rotationally symmetric functional groups. In general, they're formatted:
[substituents, alphabetical if you're a pedant] followed by [type of compound]
For example, the compound consisting of a methyl group and an ethyl group attached to an ether, ketone, or sulfide would be called "methyl ethyl ether", "methyl ethyl ketone", or "methyl ethyl sulfide" respectively.
Finally returning to the example you've given, the first compound would most commonly be referred to as "methyl tert-butyl amine" and the second compound would be called "dimethyl isopropyl amine".