When probing, you need to probe the signal where it hits the input pin, and make sure the probe ground is connected to a ground near that pin, so it doesn't hide any ground bounce. It looks to me like you're probing at the output pin, which will hide any ringing.
In the first plot, I see spikes at the signal edges. This tells me that you have some overshoot and possibly potential ringing. The fact that a 220 ohm resistor fixed it is indicative of this as well.
There are three usual solutions to this problem.
The first solution is to use a ferrite bead in series to damp the spike. The ferrite bead will look like a large resistance at high frequencies and a short at low frequencies. It's not the same as an inductor (and a spike usually means you have more than enough inductance in your line).
The second solution is to use a series resistor like you did, but typical values for this resistor are around 22 to 50 ohms, depending on the transmission line impedance, and the resistor must be placed at the source (driver output) end of the line (usually within 0.2 inch, though that may not make any difference at 62.5 kHz). The function of this resistor is to slow down the rising and falling edges of the waveform, damping their high-frequency components. 220 ohms seems like too much resistance to me. You can also use a ferrite bead (or similar EMI filter) with the resistor, usually if your line is part of a cable.
Finally, you might be able to program your driver for a slower edge rate (several nanoseconds instead of one or two), though this is still an unusual feature. This is actually the best solution, and greatly reduces EMI to boot.
Use a database
Best practice is to manage all of this information outside Altium using its database integration sub-system.
You can link symbols and footprints via a table rather than trying to manage this information inside of a symbol (which is the wrong layer of abstraction) or in a library of symbols (grouping becomes arbitrary and difficult to manage as the library size grows).
Doing it this way means that you never have to mess with internal attributes and double-entry of data.
I use CircuitHub for library management. It's free and it's trying to be a Wikipedia of parts.
It plugs into Altium (and other tools) and provides linked symbols and footprints via a local database that is sync'd from the web (so you can use it offline).
You can add/edit/manage parts on the website and it automatically (via Dropbox) syncs those changes to your computer where you can use them in Altium (or any other supported tool).
Here is how you setup CircuitHub to work in Altium.
Here are the basics of component management in CircuitHub.
I helped create CircuitHub, because I got tired of dealing with these kinds of problems in library management.
For 1 and for HyperLynx, it can be pretty good. The main differences I have seen is over/undershoot isn't as bad as the tools predict. Also some vendor's IBIS models are better than others, taking into account packaging of the IC and providing monitoring at the die pad, rather than at the IC pin/ball.
For 2, there isn't much of a difference below 1 GHz. At higher speeds HyperLynx has an option that includes lossy transmission lines.