As stated in the docs, the activation layer in keras is equivalent to a dense layer with the same activation passed as an argument.
This would be equivalent
x = Dense(64)(x)
x = Activation('relu')(x)
is equivalent to
x = Dense(8, activation='relu')(x)
As per your example if the activation layer is used as a layer, this will act as a transformation of the outputs of the previous layer.
As you can see in the model
inputs = Input(shape=(784,))
x = Dense(32, activation='tanh')(inputs)
x = Activation('relu')(x)
predictions = Dense(8, activation='softmax')(x)
The output of the first layer is the result of a densely connected layer with a tanh function. Then these outputs will each be transformed by a relu function. You can see how this is simply a transformation and does not introduce any new model parameters using
model.summary()
