When there is the call from API or Dashboard, I got this from the apache error_log file.
[2016-02-04 09:15:26] piwik.DEBUG: PluginsArchiver::callAggregateAllPlugins: Not archiving reports for plugin 'Resolution'. ["callAggregateAllPlugins","Resolution"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: PluginsArchiver::callAggregateAllPlugins: Not archiving reports for plugin 'DevicePlugins'. ["callAggregateAllPlugins","DevicePlugins"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: day archive, idSite = 1 (definitive archive), segment 'deviceType==tablet', report = 'Referrers', UTC datetime [2016-01-18 05:00:00 -> 2016-01-19 04:59:59] ["day",1,"definitive archive","deviceType==tablet","Referrers","2016-01-18 05:00:00","2016-01-19 04:59:59"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: Db::query() executing SQL: DELETE FROM piwik_archive_numeric_2016_01 WHERE idarchive = ? AND (name = 'done5f13d0ad1705fbc536687f2f24768edf.Referrers') ["query","DELETE FROM piwik_archive_numeric_2016_01 WHERE idarchive = ? AND (name = 'done5f13d0ad1705fbc536687f2f24768edf.Referrers')"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: Db::query() executing SQL: INSERT IGNORE INTO piwik_archive_numeric_2016_01 (idarchive, idsite, date1, date2, period, ts_archived, name, value) VALUES (?,?,?,?,?,?,?,?) ["query","INSERT IGNORE INTO piwik_archive_numeric_2016_01 (idarchive, idsite, date1, date2, period, ts_archived, name, value)\n VALUES (?,?,?,?,?,?,?,?)"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: Db::fetchAll() executing SQL: SELECT idarchive, value, name, date1 as startDate FROM piwik_archive_numeric_2016_01 WHERE idsite = ? AND date1 = ? AND date2 = ? AND period = ? AND ( (((name IN ('done5f13d0ad1705fbc536687f2f24768edf','done5f13d0ad1705fbc536687f2f24768edf.VisitsSummary','done5f13d0ad1705fbc536687f2f24768edf.Referrers')) AND (value IN (1,3,4)))) OR name = 'nb_visits' OR name = 'nb_visits_converted') AND ts_archived >= ? ORDER BY idarchive DESC ["fetchAll","SELECT idarchive, value, name, date1 as startDate FROM piwik_archive_numeric_2016_01\n WHERE idsite = ?\n AND date1 = ?\n AND date2 = ?\n AND period = ?\n AND ( (((name IN ('done5f13d0ad1705fbc536687f2f24768edf','done5f13d0ad1705fbc536687f2f24768edf.VisitsSummary','done5f13d0ad1705fbc536687f2f24768edf.Referrers')) AND (value IN (1,3,4))))\n OR name = 'nb_visits'\n OR name = 'nb_visits_converted')\n AND ts_archived >= ? \n ORDER BY idarchive DESC"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: Db::query() executing SQL: INSERT IGNORE INTO piwik_archive_numeric_2016_01 (idarchive, idsite, date1, date2, period, ts_archived, name, value) VALUES (?,?,?,?,?,?,?,?) ["query","INSERT IGNORE INTO piwik_archive_numeric_2016_01 (idarchive, idsite, date1, date2, period, ts_archived, name, value)\n VALUES (?,?,?,?,?,?,?,?)"] {"class":"Referrers","request_id":"25333"}
[2016-02-04 09:15:26] piwik.DEBUG: Db::query() executing SQL: INSERT IGNORE INTO piwik_archive_blob_2016_01 (idarchive, idsite, date1, date2, period, ts_archived, name, value) VALUES (?,?,?,?,?,?,?,?) ["query","INSERT IGNORE INTO piwik_archive_blob_2016_01 (idarchive, idsite, date1, date2, period, ts_archived, name, value)\n VALUES (?,?,?,?,?,?,?,?)"] {"class":"VisitTime","request_id":"0b938"}
[2016-02-04 09:15:26] piwik.DEBUG: PluginsArchiver::callAggregateAllPlugins: Initializing archiving process for all plugins [visits = 5784, visits converted = 0] ["callAggregateAllPlugins",5784,0] {"class":"Referrers","request_id":"25333"}
So, the Plugin report start to archive after that. Is there a way to include this to the console:archive?