Well, let me say that I spent about 3 days straight breeding eevees, got around 15 boxes of eevees (i release as i go of course so it doesn't get too crowded) and no shiny at all.
About 2 days ago I added a person with Eevee in their Safari, spent i'd say a day and a half in their safari and I just got a Shiny Eevee this morning from it! Also, I've found a random shiny Hawlucha and Pidgey just from seeing what kind of pokemon were in people's safaris.
I don't know if the safari has a higher chance or not but it certainly seems that way. I was using the matsuda effect through the whole process of my eevee breeding by the way.
About 2 days ago I added a person with Eevee in their Safari, spent i'd say a day and a half in their safari and I just got a Shiny Eevee this morning from it! Also, I've found a random shiny Hawlucha and Pidgey just from seeing what kind of pokemon were in people's safaris.
I don't know if the safari has a higher chance or not but it certainly seems that way. I was using the matsuda effect through the whole process of my eevee breeding by the way.