The IJN did indeed develop colored burst shells for AA purposes. The USN Technical Mission to Japan produced Report O-11, "Japanese Illuminating and Colored Burst Projectiles," which detailed the origin and nature of these type of shells. This report's introduction noted that it was not easy to find IJN officers with detailed knowledge of these type of shells, but they eventually tracked down two officers whose recollections synched up. The report indicated that these shells were used in the Type 89 12.7 cm AA mount. According to the IJN officers, the best colors were red, black, and white as they did not dissipate with sunlight and the shells used a type of red phosphorus mixed with other chemicals to achieve the effect.
As to how widespread these shells were is much less clear. The USN Technical Report speculated that not many of these shells were produced by the end of the war. The authors not only cite the few IJN personnel with detailed knowledge of these shells as evidence, but also that there were hardly any of these shells in the Home Islands' arsenals for proper evaluation. Yet the US Strategic Bombing Survey's Interrogations of Japanese Officials Q & A with Captain Kato Kenkichi, who was Musashi's executive officer in 1944, asserts that his ship received the shells:
Q. Did you use colored bursts in your anti-aircraft shells? A. Yes, each ship in the division had a different color. Red, blue, white or conventional black bursting charges were used to identify ships fire. I am uncertain when this colored ammunition first reached the fleet, but I think that it was first used in the Marianas engagement.
Kato's testimony is at odds with the the USN Technical Report's conclusions, but is congruent with its other findings such as the colors the Japanese used. While the colored shells were probably not as ubiquitous as recreations like Battle 360 or veterans' reminisces, but they were likely an element of the 1944 air battles.