Short answer. Yes, the appeal is deemed perfected as to you upon timely filing and fee payment, and the RTC loses jurisdiction once all timely appeals are perfected. Except in summary-procedure civil cases, the appeal also stays the judgment, unless the Court of Appeals, law, or the Rules provide otherwise.
What the law says
(a) Upon the timely filing of a petition for review and the payment of the corresponding docket and other lawful fees, the appeal is deemed perfected as to the petitioner. The Regional Trial Court loses jurisdiction over the case upon the perfection of the appeals filed in due time and the expiration of the time to appeal of the other parties. However, before the Court of Appeals gives due course to the petition, the Regional Trial Court may issue orders for the protection and preservation of the rights of the parties which do not involve any matter litigated by the appeal, approve compromises, permit appeals of indigent litigants, order execution pending appeal in accordance with section 2 of Rule 39, and allow withdrawal of the appeal. (b) Except in civil cases decided under the Rule on Summary Procedure, the appeal shall stay the judgment or final order unless the Court of Appeals, the law, or these Rules shall provide otherwise.
Rule 42, Section 8 — Perfection of appeal; effect thereof. Read the full provision →
When perfection occurs, and its effect on the RTC's jurisdiction
Upon the timely filing of a petition for review and the payment of the corresponding docket and other lawful fees, the appeal is deemed perfected as to the petitioner, and the Regional Trial Court loses jurisdiction over the case once the appeals filed in due time are perfected and the other parties' time to appeal has expired. This mirrors how perfection and loss of jurisdiction work for an ordinary appeal by notice of appeal, just adapted to the petition-for-review context, so a petitioner familiar with ordinary appeals will recognize the same basic timing logic here and can rely on it accordingly.
What the RTC can still do before due course is given
Even after losing jurisdiction in that sense, and before the Court of Appeals actually gives due course to the petition, the Regional Trial Court may still issue orders protecting and preserving rights not involved in the appeal, approve compromises, permit appeals of indigent litigants, order execution pending appeal under Section 2 of Rule 39, and allow withdrawal of the appeal. These residual powers keep the case from being left in limbo during the interval before the appellate court formally takes over.
The stay of judgment
Except in civil cases decided under the Rule on Summary Procedure, the appeal stays the enforcement of the judgment or final order being appealed, unless the Court of Appeals, the law, or the Rules themselves provide otherwise, meaning enforcement is generally put on hold for the duration of the appeal. The summary-procedure exception exists because those cases are meant to be resolved quickly, and allowing an automatic stay there would undercut that whole purpose, letting a losing party stall a case that the Rules deliberately designed to move fast toward a final resolution.