two load centers on one meter
100 + 100 &ne; 200

First off -- you do not need a 200A service to feed two 100A panelboards, provided the total load as determined by NEC Article 220's calculations does not exceed the service ampacity.  This is a consequence of the how 230.90(A) Exception 3 interacts with 230.40 Exception 2 and your specific setup (bold running text mine for emphasis, italics theirs):


  230.90 Where Required.
  
  Each ungrounded service conductor shall have overload protection.
  
  (A) Ungrounded Conductor. Such protection shall be
  provided by an overcurrent device in series with each ungrounded service conductor that has a rating or setting not
  higher than the allowable ampacity of the conductor. A set
  of fuses shall be considered all the fuses required to protect
  all the ungrounded conductors of a circuit. Single-pole circuit breakers, grouped in accordance with 230.71(B), shall
  be considered as one protective device.
  
  Exception No. 1: For motor-starting currents, ratings that
  comply with 430.52, 430.62, and 430.63 shall be permitted.
  
  Exception No.2: Fuses and circuit breakers with a rating
  or setting that complies with 240.4(B) or (C) and 240.6
  shall be permitted.
  
  Exception No.3: Two to six circuit breakers or sets of
  fuses shall be permitted as the overcurrent device to provide the overload protection. The sum of the ratings of the
  circuit breakers or fuses shall be permitted to exceed the
  ampacity of the service conductors, provided the calculated
  load does not exceed the ampacity of the service
  conductors.
  
  Exception No.4: Overload protection for fire pump supply
  conductors shall comply with 695.4(B)(2)(a).
  
  Exception No.5: Overload protection for 120/240-volt,
  3-wire, single-phase dwelling services shall be permitted in
  accordance with the requirements of 310.15(B)(7).


(Note that exception 5 has to do with the 310.15(B)(7) allowances for residential service conductor sizing -- they need to be taken into account when determining the total ampacity of your service and the ampacity of your individual sets of service entrance conductors, but stop there.)

A tale of a misplaced panelboard

But, there's more! While what the electrician did (putting a second main panel on your service) would have been OK when done properly as it would fall under 2014 NEC 230.40, exception 2 (bold running text mine for emphasis, italics theirs):


  230.40 Number of Service-Entrance Conductor Sets.
  
  Each service drop, set of overhead service conductors, set
  of underground service conductors, or service lateral shall
  supply only one set of service-entrance conductors.
  
  Exception No.1: A building with more than one occupancy shall be permitted to have one set of service-
  entrance conductors for each service, as defined in 230.2,
  run to each occupancy or group of occupancies. If the
  number of service disconnect locations for any given classification of service does not exceed six, the requirements of
  230.2(E) shall apply at each location. If the number of
  service disconnect locations exceeds six for any given supply classification, all service disconnect locations for all
  supply characteristics, together with any branch circuit or
  feeder supply sources, if applicable, shall be clearly described using suitable graphics or text, or both, on one or
  more plaques located in an approved, readily accessible
  location(s) on the building or structure served and as near
  as practicable to the point(s) of attachment or entry(ies) for
  each service drop or service lateral, and for each set of
  overhead or underground service conductors.
  
  Exception No.2: Where two to six service disconnecting
  means in separate enclosures are grouped at one location
  and supply separate loads from one service drop, set of
  overhead service conductors, set of underground service
  conductors, or service lateral, one set of service-entrance
  conductors shall be permitted to supply each or several
  such service equipment enclosures.
  
  Exception No.3: A single-family dwelling unit and its
  accessory structures shall be permitted to have one set of
  service-entrance conductors run to each from a single service drop, set of overhead service conductors, set of underground service conductors, or service lateral.
  
  Exception No.4: Two-family dwellings, multi-family dwellings, and multiple occupancy buildings shall be permitted
  to have one set of service-entrance conductors installed to
  supply the circuits covered in 210.25.
  
  Exception No.5: One set of service-entrance conductors
  connected to the supply side of the normal service disconnecting means shall be permitted to supply each or several
  systems covered by 230.82(5) or 230.82(6).


However, your electrician screwed up when he put the second panel on the outside of your garage, as that ruins the grouping required by 230.40, exception 2 and 230.72(A):


  230.72 Grouping of Disconnects.
  
  (A) General. The two to six disconnects as permitted in
  230.71 shall be grouped. Each disconnect shall be marked
  to indicate the load served.


So, in any case, you'll need to have the electrician move the second panelboard inside to a spot next to where the first one lives, or replace the first panelboard with an exterior unit that can be mounted next to where the new one lives.