Update 3.
Having "organizations: org1" for your user1 in fixtures seed data - seems this is causing the issue, because user can be connected to organization only through your joint table. 
I didn't find anything explicit in spec, but something relevant here
Fixtures bypass the normal Active Record object creation process.
  After reading them from YAML file, they are inserted into database
  directly using insert query. So they skip callbacks and validations
  check. This also has an interesting side-effect which can be used for
  drying up fixtures.
Update 2. 
I was wrong at assumption that you can't have timestamps in has_and_belongs_to_many jointable managed by Rails. In fact, inside HasAndBelongsToMany Rails will create an ActiveRecord::Base class for that table - here
def through_model
   habtm = JoinTableResolver.build lhs_model, association_name, options
   join_model = Class.new(ActiveRecord::Base) {
     class << self;
     ...
And ActiveRecord::Base include Timestamp module
So your error should be caused by some other way of creating an entry in jointable other then standard Rails association.
Original.
I don't believe that you can have automatically managed timestamp fields in jointable for has_and_belongs_to_many relation in ActiveRecord. This didn't (intentionally) work in old Rails (e.g. 3.2 - link below), and it don't sound like it changed recently.
If you want to have extended join table, you may create a dedicated ActiveRecord model for it and use use has_many :through association. This way it will automatically support timestamps should you add it to table definition.
See https://github.com/rails/rails/issues/4653 for timestamps on HABTM jointable
AFAICT Rails 3.1 does not populate timestamps on a join table. The
  only difference is that in 3.2, when you add timestamps, they are
  marked as NOT NULL.
@veganstraightedge the timestamps didn't "work" in 3.1 - they just
  didn't raise an error when the join table was saved with them as null.
  the difference here is that in 3.2 timestamps are created with a NOT
  NULL constraint.
Basically, this can come from an idea that you don't have ActiveRecord model class for the jointable (update 2 - actually you have!), and timestamps are feature of ActiveRecord model. Timestamps in Rails 5.0rc1 hasn't changed a lot - sources - Timestamp is a module that extends ActiveRecord class.
By the way, it's now suggested to use create_join_table migration helper that will create "pure" table (two id's only, no timestamps):
https://github.com/rails/rails/pull/4726
SO Question with similiar error - Rails 3.2 + MySQL: Error: Field 'created_at' doesn't have a default value: INSERT INTO
Rails 3.2 doesn't automatically populate the timestamp fields for join
  tables of :habtm relationships.
Alternatively (warning - theory!), you can try using either Association callbacks or Association extensions - http://api.rubyonrails.org/classes/ActiveRecord/Associations/ClassMethods.html
Association callbacks
Similar to the normal callbacks that hook into the life cycle of an
  Active Record object, you can also define callbacks that get triggered
  when you add an object to or remove an object from an association
  collection.
class Project
  has_and_belongs_to_many :developers, after_add: :evaluate_velocity
  def evaluate_velocity(developer)
    ...
  end
end
Extensions
The extension argument allows you to pass a block into a
  has_and_belongs_to_many association. This is useful for adding new finders, > creators and other factory-type methods to be used as part of
  the association.
has_and_belongs_to_many :contractors do
  def find_or_create_by_name(name)
    first_name, last_name = name.split(" ", 2)
    find_or_create_by(first_name: first_name, last_name: last_name)
  end
end
Extensions can refer to the internals of the association proxy using
  these three attributes of the proxy_association accessor:
proxy_association.owner returns the object that the association is a part of. 
proxy_association.reflection returns the reflection object that describes the association. 
proxy_association.target returns the associated object for belongs_to or has_one, or the collection of associated objects for has_many or has_and_belongs_to_many.