Permission on reproduction of data extracted from a figure
I plot the raw data together with mine


The plot is yours, the data is theirs. 


  If I publish this plot and properly cite their paper, do I need to ask them for permission? 


No, the citation (and suitable explanation) suffices to attribute the data source. Indeed, as noted by the referenced source (under the heading Reuse of graphs/tables...):

...reuse of raw data does not generally need permission, provided you have plotted 
it into a different graph/table. You should however cite the source of the data.