Tested on Mongoid 3.1.6.
Let's do some preparations:

class Foo
include Mongoid::Document
embeds_many :bars
end

class Bar
include Mongoid::Document
embedded_in :foo
before_save :baz
field :qux, type: String
def baz
puts "baz launch"
end
end

foo = Foo.new
foo.bars << Bar.new

foo.save

MOPED: 127.0.0.1:27017 INSERT database=overmind_development collection=foos documents=[{"_id"=>"5375c10f32178c4d27000004", "bars"=>[

{"_id"=>"5375c10f32178c4d27000005"}

]}] flags=[] (0.1349ms)

Now if we change and save the embedded object, we'll get the callback:

foo.bars[0].qux = "hoge"
foo.bars[0].save
baz launch
MOPED: 127.0.0.1:27017 UPDATE database=overmind_development collection=foos selector=

{"_id"=>"5375c10f32178c4d27000004", "bars._id"=>"5375c10f32178c4d27000005"}

update={"$set"=>{"bars.$.qux"=>"hoge"}} flags=[] (0.6673ms)

But if we do save of the main object, the callback isn't run:

foo.bars[0].qux = "piyo"
foo.save
MOPED: 127.0.0.1:27017 UPDATE database=overmind_development collection=foos selector=

{"_id"=>"5375c10f32178c4d27000004"}

update={"$set"=>{"bars.0.qux"=>"piyo"}} flags=[] (0.1249ms)

This makes using callbacks on embedded objects pretty useless. I think that if you save the main object, then all the modified embedded objects must have their callbacks run.