I've figured it out.
It all revolves around [this](https://github.com/GluuFederation/oxAuth/issues/340) issue/enhancement reported/proposed by Michael earlier. He refers to [Section 5.4](http://openid.net/specs/openid-connect-core-1_0.html#ScopeClaims) of OIDC Core spec, which states:
>The Claims requested by the profile, email, address, and phone scope values are returned from the UserInfo Endpoint, as described in Section 5.3.2, when a response_type value is used that results in an Access Token being issued. However, when no Access Token is issued (which is the case for the response_type value id_token), the resulting Claims are returned in the ID Token.
In Gluu packages prior to this enhancement oxAuth would have **always** included all claims requested via scopes in `id_token` too. After this enhancement, the only case when anything except for a set of mandatory claims would have been included in the `id_token` was when `response_type` used wouldn't allowed subsequent request to token/userinfo endpoints, i.e. when no authz code or access token is returned in response from authz endpoint, like in case of `response_type=id_token`, used by implicit flow.
Michael also proposed to add a new oxAuth's setting `legacy_id_token_claims=true` to preserve legacy behaviour, to facilitate migration to the new version.
In my SP2 instance this setting has value "true", and in the mentioned SP1 instance it isn't included in list of settings, what, I suppose, means that a default behaviour (the new one) is in effect. I've tested it by using `response_type=id_token` in request to its authz endpoint, and indeed I got `id_token` with all my claims in response to this request.
So, shortly, you are advised to use userinfo endpoint to get all your usual claims whenever it's possible (and that's possible for most of flows defined by OIDC). But if you really need to have them in `id_token` for other flows too, you could try to set `legacy_id_token_claims` to "true" (no guarantee this hack will not be removed in future versions, though, as this is against specs)