When I completed my first eligible Mindshifting May exercise it seems like I immediately got awarded the badge.
Looking at the code for the badge awarder it seems only the month is checked:
def award_to?(user) user.solutions.published.joins(exercise: :track). where('tracks.slug': TRACK_SLUGS). where(' (MONTH(published_at) = 4 AND DAY(published_at) = 30) OR (MONTH(published_at) = 5) OR (MONTH(published_at) = 6 AND DAY(published_at) = 1) '). where.not('exercises.slug': 'hello-world'). count >= 5 end
AFAIR I did a good chunk of the Pharo track a year (or two?) ago, so it would appear that these exercises actually were counted for the badge.