I understand what you are saying but I think you have the order wrong. The article where Travis was praising NGLA came first. There was a well-publicized members tournament at NGLA in July of 1910, and and the excerpt above (in blue) is from the AG article on NGLA in the August 1910 issue of American Golfer. The other articles - where Travis becomes critical - are from late 1912 and early 1913.
So what changed? At least two things happened in the fall of 1910 which seemed to have really set Travis (and others) off:
1. In September 1910, the R&A banned mallet putters, including the popular Schenectady putter which Travis had used to win the British Amateur 6 years before. I won't get into it here, but this created a huge stir in American golf and fueled strong sentiments against the R&A and what was portrayed as British paternalism and condescension. CBM, who was the only American on the R&A rules committee, ended up trying to broker peace which would have preserved a single set of rules, but the result was that much of the hostility toward the ruling ended up being directed at him. Travis was leading this charge. And he and CBM went back and forth on the issue.
2. Also, in November 1910, Horace Hutchinson published an article entitled "An English View of American Golf" in H.J. Whigham's Metropolitan Magazine. Hutchinson was considered close to CBM and Whigham (who was from a prominent golfing family in Prestwick, had been very involved in the creation of NGLA with CBM, and was his son-in-law.) In the article, Hutchinson is somewhat critical of many of the leading American courses, but heaped praise on CBM's NGLA. Perhaps unfairly, the article was viewed as a slap in the face of American golf.
Given the Schenectady putter fiasco, the timing couldn't have been worse. To put it mildly, a segment of the American Golfing community were very upset by the comments and read it as another shot at American golf and at American's generally. Much of the hostility was expressed in Travis's magazine, with Travis seemingly at the middle of it. There was a letter/article written by "Americus" trashing Hutchinson, and given that NGLA had escaped criticism from Hutchinson, CBM and NGLA seemed to be targets as well. I don't know whether or not Travis was in fact "Americus," but he certainly was egging him on, even publishing an editorial comment adding to the critique. There were also calls for reforms to the USGA which was considered to chummy with the R&A and not representative enough of the outlying clubs.
Anyway, it gets pretty complicated, but this seems to have lead to a strong anti-british sentiment and a strong anti-CBM sentiment by Travis and probably some others. It was still ongoing a few years later, when AG went after NGLA after the tournament with the high scores. And it continued in the Amateur Rule crisis a few years later.
Note, this isn't intended to be the final word on any of this, just a quick and dirty assessment to try to set out some of the potential issues between Travis and CBM and a certain segment of the golfing establishment.