NYC keeps going up while Austin has clearly reversed the upward trend. It seems you may have not looked at the graphs you linked.
Austin: 346 -> 510. 510/346 = 1.47
Dallas: 192-> 295. 295/192= 1.53
NYC: 203-> 318. 510/346 = 1.56
SF: 271-> 361. 510/346 = 1.33
LA: 291-> 443. 510/346 = 1.52
These numbers are all pretty close imo, clustered around 50% growth in the last 5 years. Austin in particular grew 47% over the last 5 years, for a annualized growth rate of ~8% -- that is some _crazy_ growth for real estate, when the long term average in the US is about 3% annualized. IMO SF is the only remarkable datapoint, with 33% growth -> ~6% annualized growth. Even that is still high though.
It would be easier to visualize if we can plot them all on top of each other, but I didn't find an easy way to do that.
Austin: 502-> 510 growth: 1.6%
Dallas: 263-> 295 growth: 12.2%
NYC: 255-> 318 growth: 24.7%
SF: 349-> 361 growth: 3.4%
LA: 384-> 443 growth: 15.4%
"Lies, damn lies, and statistics."
However, my interpretation of the original claim about Austin is "Austin house prices have grown less in the last 5 years than other places". That claim is pretty specific, and can be examined by looking at just the start and end points. Looking at the end points, it seems incorrect.
800/346=2.3
2.3 >> 1.47
That's not a wobble in the plot.